Question

Suppose that there are two types of employees: Narutos and Sasukes. Employers cannot distinguish between the two types during a job. interview, but they value Narutos more because everyone is more productive around them. Assume that the value of a Sasuke-type employee is $10 and the value of a Naruto type is $20. Also assume that the cost of education for a Sasuke is 2.5y and the cost of education for a Naruto is 2y, where y is years of education. If Narutos make up 25% ofthe population:

a. What is the pooling equilibrium wage?
b. What values of y will lead to a separating equilibrium?

Answer 1

Step-by-step explanation:

From the given information:

The average wage is expected to be paid to both workers since it is difficult tot distinguish between the two types.

w_s = 10

w_N = 20

ω_s = 2.5y

ω_N = 2y

proportion of N types (λ) = 0.25

proportion of S types (1-λ) = 0.75

Thus, the pooling wage = λ_Nw_N + λ_Sw_S

= (0.25 × 20) + (0.75 × 10)

= 5.0 + 7.5

= $12.5

(b)

The separating equilibrium can be computed as follows:

N-type ( High type) : w_N- w_S > ω_N

= 20 - 10 > 2y

2y < 10

y < 5

For an S-type (low type); the cost of education needs to be greater than the increment in wages if the education is acquired.

w_N- w_S > ω_S

If education is acquired, S-type will get wages as of N-types

Thus;

20-10 <2.5y

10 < 2.5y

y > 4

Hence, the value of y= (4,5)